Add the flours, yeast, salt, sugar, butter, egg, and milk to a deep bowl. Using your fingertips, stir to combine, then knead it a few times until it comes together into a shaggy dough.

Dust a counter with flour. Drop the dough onto the counter, and knead until it forms a smooth dough—this takes about 10 minutes.

Coat a deep bowl with oil or cooking spray. Place the dough in the bowl, and cover tightly. Set in a warm spot until just about doubled in volume, about 60 to 75 minutes (it won’t get as puffy as traditional English muffin dough).

Dust a counter with more flour and some semolina. Roll the dough out to ¾ to 1-inch thickness (2 to 3 cm). Use a 3-inch (8-cm) ring to cut out rounds of dough. You should get 6 to 8 pieces depending on how thick you roll it. It’s okay to re-roll the scraps once.

Dust a sheet pan with semolina. Place the cut out muffins on the pan, and cover with plastic film. Let sit in a warm spot for 30 minutes, until they’ve puffed up.

About 5 minutes before the proofing is done, heat a 10-inch (25-cm) cast iron skillet over the lowest heat setting until the pan is hot. Place 3 to 4 muffins in the pan. Cook for about 5 minutes, until puffed up slightly, and nicely browned on the bottom. Flip, and cook for about 5 minutes more. Transfer to a wire rack to cool.

Repeat with the remaining muffins, keeping a closer eye—the pan will be quite hot, and might only need 4 minutes per side with each successive batch.